ECC—Error-Correction-Coding is a process by which additional redundant information is appended to a message in order to render the message resilient to errors inflicted on it in the process of transmission and reception or equivalently, during storage and retrieval. This additional information is called the “redundancy.” There are many various ways and algorithms to derive the redundancy, the exact algorithm is not pertinent to this invention, it is enough to note, that the redundancy is computed by the encoder from all of the message's bits.
In the decoder a reverse process occurs, the erroneous message with the redundancy is received and inspected. The errors are identified and fixed (if possible), the redundancy is stripped from the message, and the recovered message is passed to the client.
In multi-dimensional encoding, a stream of data is passed through the set of multiple component encoders, which together encode the full payload into a single codeword. It is well known that BCH encoding may be done by using a shift register through which the systematic data is passed. Therefore, that data simply passes through the component encoders without being modified while the shift-register advances. When the systematic data of the code completely passed through the shift-register, the content of the shift register is the redundancy of the code and is appended to the data stream. This principle works for all component encoders in all dimensions.